THE  ANEROID  BAROMETER,  ITS  THEORY  AND 
ITS  USE,  WITH  SPECIAL  REFERENCE  TO  THE 
DETERMINATION  OF  ALTITUDES. 


BY 


E.  A.  GIESELER,  C.  E. 


(Reprinted  from  the  Journal  of  the  Franklin  Institute,  November,  1889,; 


PHILADELPHIA  ; 


\ 

) 


CM 


ivio  i  ,  .., 


at 


Oak  Btre^ 


The  aneroid  BAROMETER,  its  VARIOUS  FORMS, 
ITS  THEORY  AND  ITS  USE,  with  SPECIAL 
REFERENCE  to  the  DETERMINA¬ 
TION  OF  ALTITUDES. 


By  E.  a.  Gieseler,  C.E. 


I.  GENERAL  DISCUSSION. 

The  motor  of  all  aneroids  consists  in  an  hermetically 
sealed  box,  the  air  of  which  has  been  exhausted  as  com¬ 
pletely  as  practicable,  and  the  flexible  sides  of  which  will 
consequently  perform  certain  motions,  when  the  pressure  of 
the  atmosphere  changes.  These  motions  are,  however,  too 
small  to  be  perceived  by  the  unaided  eye,  and  they  are, 
therefore,  transmitted  to  a  suitable  mechanism,  by  means  of 
which  they  are  magnified  to  such  an  extent  that  they  can 
be  discerned  and  measured. 

The  invention  of  the  aneroid  dates  back  to  the  beginning 
of  this  century,  one  of  the  oldest  forms  being  the  one  con- 


44098 


2 


structed  by  Bourdon,  in  which  the  box  has  the  shape  of  a 
tube  sealed  at  both  ends,  and  bent  into  the  shape  of  a  circle. 
A  small  open  space  remains  between  the  two  ends,  and  dia¬ 
metrically  opposite  this  gap  the  tube  is  fastened  to  a  sup¬ 
porting  plate.  The  cross-section  of  this  tube  is  either  rec¬ 
tangular  or  oval,  and  the  direction  of  its  greatest  height  or 
diameter  stands  at  right  angles  to  the  plane  of  the  circle 
into  which  the  tube  has  been  bent,  which  is  parallel  to  the 
supporting  plate. 

When  compressed  air  or  steam  is  admitted  into  such  a 
tube,  the  inner  pressureThus  created  will  have  the  tendency 
to  straighten  it,  on  account  of  the  excess  of  pressure  exer¬ 
cised  on  the  greater  area  of  the  outer  circular  side  as  com¬ 
pared  with  the  smaller  area  of  the  inner  circular  side.  Any 
increawSe^'of  the  inner  pressure  will  result  in  a  further  flatten¬ 
ing  of  th^,' circle  into  which  the  tube  has  been  bent,  while  a 
decrease  of  it  will  cause  such  curve  to  be  sharpened. 

Precisely  the  reverse  will  take  place,  when  the  tube  has 
been  exhausted,  because  then  the  acting  force,  instead  of 
being  an  inside  pressure,  will  be  the  outside  pressure  of  the 
atmosphere.  The  tube  being  held  as  described  before  at 
one  point  only,  which  is  situated  diametrically  opposite  the 
opening  between  the  two  ends,  it  is  evident  that  the 
changes  of  form  of  the  curve  must  result  in  movements  of 
these  ends ;  under  the  influence  of  high-  atmospheric  pres¬ 
sure  they  will  approach  each  other,  while  a  decrease  of  pres¬ 
sure  will  widen  the  gap  between  them.  The  movements  of 
the  ends  are  transmitted  by  a  simple  arrangement  to  a  hand 
pointing  on  a  graduated  dial.  They  are  magnified  either 
by  levers  acting  on  the  short  arm  of  the  hand  or  pointer,  or, 
when  the  latter  is  mounted  centrally,  by  means  of  a  toothed 
wheel  and  pinion. 

This  form  of  the  aneroid  has  nowadays  been  entirely 
superseded  by  others,  in  which  the  vacuum  box  has  the 
shape  of  a  flat  cylinder,  into  the  upper  and  lower  circular 
ends  of  which  concentric  grooves  are  pressed  in  order  to 
equalize  the  motions  performed  by  them  under  the  influence 
of  the  varying  atmospheric  pressure.  To  the  side  of  the 
vacuum  box  is  soldered  a  small  tin  pipe,  through  which  the 


3 


air  is  exhausted.  After  this  has  been  done  the  pipe  is  sealed 
and  the  upper  and  lower  ends  of  the  box  are  now  deflected 
towards  its  interior  by  the  pressure  of  the  atmosphere,  the 
amount  of  such  deflections  for  a  given  pressure  being 
dependent  on  the  strength  of  the  plates.  This  must  be 
sufficient  to  prevent  too  great  a  departure  from  the  horizon¬ 
tal  positions,  in  order  not  to  strain  the  plates  beyond  their 
limit  of  elasticity.  The  movements  are,  therefore,  neces¬ 
sarily  small ;  a  fall  of  of  an  inch  in  the  mercurial  barom¬ 
eter  corresponding  to  an  approach  of  about  of  an  inch 

of  the  plates  of  the  vacuum  chamber. 

II.  THE  NAUDET  ANEROID. 

To  measure  such  exceedingly  small  quantities,  one  class 
of  modern  aneroids  is  provided  with  an  ingenious  mechan¬ 
ism  invented  by  Vidi  and  later  improved  by  Naudet,  the 
main  parts  of  which  are  shown  in  Fig.  /. 


To  the  base  or  foundation  plate  B  B  are  firmly  attached 
a  laminated  spring's  and  the  vacuum  chamber  V.  The  latter 
carries  upon  its  centre  an  upright  pillar  P,  which  passes 
through  an  opening  in, the  spring  and  presses  on  its  upper 
side  by  means  of  the  knife  edge' A.  An  elastic  system  is  in 
this  way  formed  by  vacuum  chamber  and  spring  and  the 
pulsations  of  the  former  will  be  imparted  to  the  latter.  The 
horizontal  arm  A  is  firmly  attached  to  the  spring  and  will 
therefore  follow  its  movements.  These  will  appear  in  a 
magnified  scale  at  the  end  L  and  are  transmitted  by  the  two 
links  L  and  L'  to  the  rocker  shaft  which  turns  in  bearings 
attached  to  the  base  plate,  but  not  shown  in  the  diagram. 
The  turning  motions  of  R  are  further  magnified  by  the  arm 
A’  and  thence  transmitted  by  a  small  chain  Cto  the  central 
shaft  /,  which  carries  the  index  pointer.  The  required  ten- 
vsion  on  the  chain  is  produced  by  a  spiral  spring  acting  on 


4 


the  central  shaft.  This  spring  and  the  bearings  for  the  cen¬ 
tral  shaft  are  not  shown  in  the  diagram. 

The  graduation  of  the  dial  on  which  moves  the  index 
pointer,  like  the  hand  on  a  watch  dial,  is  made  to  correspond 
as  nearly  as  possible  with  the  reading  of  the  mercurial 
barometer,  and,  like  the  latter,  is  expressed  in  millimetres 
or  in  inches.  Perfect  accuracy  in  this  respect  cannot  be 
attained ;  there  will  always  be  required  a  certain  correction 
for  graduation.  This  and  the  corrections  for  temperature 
are  the  most  important  ones  for  practical  work  and  will  be 
discussed  further  below. 

As  apparent  from  the  above,  the  use  of  the  Naudet  ane¬ 
roid  is  very  simple ;  in  fact,  the  handling  and  reading  of  no 
instrument  could  be  simpler.  But  this  advantage  is  obtained 
by  means  which,  in  themselves,  constitute  the  source  of 
undoubted  defects.  The  magnification  and  the  measuring 
of  the  small  movements  of  the  vacuum  chamber  are  per¬ 
formed  by  means  of  an  exceedingly  delicate  mechanism, 
which  is  liable  to  get  out  of  order  unless  great  care  is  exer¬ 
cised  in  handling  and  transporting  the  instrument.  Such 
constant  and  unremitting  care,  however,  cannot  be  exercised 
under  all  circumstances,  especially  not  in  our  country  where 
the  aneroid,  in  the  hands  of  the  railroad  engineer  for 
instance,  is  frequently  subjected  to  swift  transportation  on 
horseback  over  many  miles  of  rough  country,  the  jolting  and 
jarring  of  which  are  almost  certain  to  prove  injurious  to  the 
instrument.  Even  ordinary  transportation  in  good  packing 
frequently  puts  a  Naudet  out  of  working  order,  and  no  dealer 
in  these  instruments  can  warrant  their  safe  arrival  at  the 
end  of  a  long  railroad  journey. 

Hence  the  frequent  complaints  of  engineers,  who  have 
bought  instruments  in  New  York  or  some  other  great  centre 
and  to  their  dismay  find  them  giving  out  completely  when 
needed,  a  calamity  which  will  be  all  the  more  annoying, 
when  it  happens,  as  it  naturally  often  does,  at  a  place  far 
removed  from  any  facilities  for  repairing. 

Aside  from  such  heavy  shocks,  which  may  at  once  render 
a  Naudet  perfectly  useless,  an  instrument  actually  used  in 
the  field  is  necessarily  exposed  to  small  shocks,  which  even 


5 


the  most  careful  and  experienced  observer  cannot  entirely 
avoid,  and  the  continuance  of  which  tends  to  produce  a- 
slackening  of  the  mechanism.  The  gradual  deteriorating 
from  this  cause  of  Naudet  aneroids,  during  their  use  in  the 
field,  is  a  well-established  fact,  even  when  they  are  in  the 
hands  of  the  best  observers  (Report  of  Mr.  J.  Campbell, 
R.  N.,  published  in  U.  S.  Monthly  Weather  Review,  September 
1879). 

Finally  a  very  important  defect  .should  be  mentioned 
here,  which  may  not  inadequately  be  termed  the  “  elastic 
reaction  ”  of  the  instrument  and  which  asserts  itself  in  the 
tardiness  with  which  the  mechanism  accommodates  itself 
to  changes  in  atmospheric  pressure. 

C.  Kroeber,  in  his  experiments  with  Naudet  aneroids 
{Zeitschrift  fiir  Verniessiingswesen,  Heft.  8,  1881),  has  found  that 
it  took  the  instrument  about  two  days  to  accommodate  itself 
to  a  change  of  pressure  corresponding  to  five  inches  of  the 
mercurial  column,  the  readings  taken  immediately  after  the 
pressure  had  been  changed  differing  nearly  two-tenths  of 
an  inch  from  the  final  ones.  If  not  considered  in  the  case 
of  a  measurement  of  altitudes  this  difference  would  have 
constituted  an  error  of  about  200  feet  in  about  5,000  feet. 

It  is  true  that  the  quality  of  “  elastic  reaction  ”  in  a 
measure  is  common  to  all  aneroids,  but  it  is  especially  pro¬ 
nounced  in  the  Naudet,  on  account  of  its  peculiar  and  com 
plicated  mechanism.  As  apparent  from  the  above,  the  latter 
circumstance  constitutes  the  origin  of  several  serious 
defects,  the  only  remedy  for  which,  evidently  consists  in  a' 
simplification  of  the  mechanism. 

But  it  is  as  evident  that  such  a  simplification  could  not 
be  attained,  without  at  the  same  time  sacrificing  in  a  meas¬ 
ure  the  ease  and  simplicity  of  handling  and  reading  the 
instrument.  Some  of  the  work,  which  in  the  Naudet  aner¬ 
oid  is  performed  by  the  complicated  mechanism  itself,  in  an 
instrument  of  simpler  construction  necessarily  had  to 
devolve  on  the  observer.  The  difficulty  then,  con.sisted  in 
harmonizing,  in  the  most  advantageous  manner  possible, 
requirements,  the  fulfilment  of  one  of  which  impaired  the 
fulfilment  of  the  other. 


6 


III.  THE  GOLDSCHMID  ANEROID. 


This  problem  was  solved  after  years  of  experiments  by 
J.  Goldschmid,  of  Zurich,  about  i860,  through  an  entirely 
novel  construction,  in  which  the  movements  of  the  vacuum 
chamber  are  measured  by  a  micrometer  screw  acting  on  a 
peculiar  lever  arrangement,  combined  with  optical  magnifi¬ 
cation.  In  the  following  diagram,  the  left-hand  side  of 
which  represents '  a  section  through  the  instrument,  the 
exceedingly  simple  arrangement  of  the  working  parts  is 
clearly  shown. 

To  the  centre  of  the  top  of  the  vacuum  chamber  A  A  is 
soldered  a  crank-shaped  piece,  which  ends  at  one  extremity 
in  an  upward  turned  knife  edge  ;  the  latter  supports  the 
main  lever  e  e'\  which  in  its  turn  swings  freely  around  the 
fulcrum  e".  The  movements  of  the  vacuum  chamber  are 


Fig.  2 


transmitted  by  the  supporting  knife  edge  to  the  main  lever, 
the  end  e  of  which  carries  a  small  hammer-shaped  piece. 
On  the  face  of  this  is  marked  a  horizontal  index  line,  which 
will  move  vertically  up  and  down,  according  to  the  varying 
pressure  of  the  atmosphere.  These  movements  take  place 
alongside  of  a  vertical  ivory  scale,  which  serves  to  measure 
them  and  which  bears  a  graduation  corresponding  to  the 
full  inches  of  the  mercurial  column  (see  the  right-hand  side 
of  Fig.  a,  which  shows  the  hammer  and  scale  in  front  view). 

While  from  the  ivory  scale  the  full  inches  only  of  the 
aneroid  reading  can  be  taken,  the  following  arrangement 
serves  for  measuring  the  tenths  and  hundredths  of  inches. 
A  fine  and  light  spring  e'  e”  is  soldered  to  the  main  lever 
near  the  end  e" ;  at  the  other  end  e'  it  carries  a  small  ham¬ 
mer,  similar  to  the  one  described  before ;  when  no  pressure 
is  exercised  on  the  spring  this  hammer  is  held  by  the  elas- 


7 


ticity  of  the  same  a  little  above  the  top  of  the  hammer 
standing  at  the  same  time  sideways  of  it. 

To  the  cover  T  T,  of  the  brass  case  enclosing  the  entire 
apparatus,  is  attached  the  micrometer  screw  M,  which  can 
therefore  be  screwed  up  or  down  by  turning  such  cover. 
The  lower  pointed  end  of  the  micrometer  acts  on  the  spring 
£'  e",  and  when  a  reading  is  to  be  taken  it  is  screwed  down 
until  the  spring  has  been  depressed  so  much  that  the  index 
line  of  e'  coincides  with  the  index  line  of  e. 

It  is  at  once  clear  that  this  position  of  the  two  hammers, 
which  is  shown  in  the  diagram,  corresponds  to  a  certain  dis¬ 
tance  between  the  point  of  the  micrometer  screw  and  the 
main  lever,  a  distance  which  remains  the  same  for  all  the 
various  positions  into  which  the  main  lever  may  be  raised 
or  lowered  by  the  movements  of  the  vacuum  box.  The 
point  up  to  which  the  micrometer  screw  has  to  be  screwed 
down,  in  order  to  make  the  two  index  lines  coincide,  is  thus 
made  a  measure  of  the  position  in  altitude  of  the  main 
lever.  This  measure  is  read  by  means  of  a  graduation 
■engraved  on  the  circumference  of  the  cover  and  dividing 
the  same  into  loo  equal  parts,  each  of  which  corresponds  to 
one  hundredth  of  an  inch  of  mercurial  barometer  height. 
The  graduation  is  so  wide  that  thousandths  can  easily  be 
estimated. 

The  modus  operandi  then,  in  using  the  Goldschmid 
aneroid,  is  as  follows : 

The  outer  morocco  case  of  the  instrument  is  opened,  and 
holding  the  latter  in  a  horizontal  position  the  cover  is 
screwed  down,  whiie  at  the  same  time  the  two  little  ham¬ 
mers,  protruding  from  the  brass  case  through  a  window-like 
opening,  are  observed  by  means  of  the  attached  microscope. 
When  the  upper  hammer  is  seen  to  commence  moving 
downward,  then  the  micrometer  screw  should  be  turned 
carefully  and  slowly,  and  when  the  two  index  lines  coincide 
it  is  stopped  entirely.  Before  such  coincidence  is  obtained 
the  instrument  should  be  tapped  lightly  on  the  top,  in  order 
to  eliminate  any  inertia  of  the  mechanism.  It  is  very 
important  that  this  tapping  should  always  be  done  in  the 
same  position  of  the  hammers,  because  if,  for  instance,  it  is 


8 


done  sometimes  before  coincidence  and  at  other  times  at 
coincidence,  then  differences  in  the  readings  will  be  the  con¬ 
sequence,  that  may  amount  to  as  much  as  yj-g-  of  an  inch. 
In  order  to  insure  uniformity  in  this  respect  it  is  advisable 
to  make  it  a  standing  rule,  to  tap  ivheii  the  lower  edge  of  the 
upper  hammer  arrives  at  coincidenee  with  the  index  line ;  thence 
forward  the  screw  should  be  turned  very  carefully,  avoiding 
all  further  shocks. 

IV.  DISCUSSION  OF  THE  CORRECTIONS. 

In  order  to  find,  from  the  reading  obtained  by  a  Naudet 
or  a  Goldschmid  aneroid,  the  height  of  the  mercurial  column 
of  32°  Fahrenheit  temperature,  corresponding  to  the  same 
pressure,  three  corrections  are  required,  viz  :  for  tempera¬ 
ture,  for  graduation  and  for  position,  the  latter  not  being 
required  when  the  instrument  is  used  for  measuring  alti¬ 
tudes  only. 

Let  ^  represent  the  reading  of  the  aneroid,  F  the  tem¬ 
perature  of  the  instrument  in  degrees  Fahrenheit,  and 
the  reading  that  would  have  been  obtained  if  the  tempera¬ 
ture  had  been  32°  Fahrenheit,  then  we  have,  concerning  the 
correction  for  temperature : 

A,=AfaF{f)  (I) 

wherein  a  is  the  coefficient  for  temperature,  the  structure  of 
the  function  t  for  the  present  remaining  undecided. 

Regarding  the  correction  for  graduation,  aneroids  are 
generally  set  so,  that  at  a  reading  of  thirty  inches  there  is 
coincidence  between  them  and  the  mifercurial  barometer, 
after  the  correction  for  temperature  has  been  made  on  both. 
The  coefficient  of  graduation  is  the  difference  between  one 
inch  of  the  mercurial  column  and  one  inch  of  the  aneroid 
graduation :  this — multiplied  by  the  difference,  thirty — read¬ 
ing,  clearly  renders  the  correction  for  graduation.  Hence 
we  have 

(.30- A,) 

wherein  the  height  of  the  mercurial  column  reduced  to- 
the  freezing  point  and  ^9  the  coefficient  for  graduation. 


9 


The  above  described  coincidence  between  the  aneroid 
and  the  mercurial  at  thirty  inches,  even  if  completely 
attained,  rarely  lasts  long,  and  in  order  to  compensate  for 
this  a  constant  must  be  added  to  the  right-hand  side  of  the 
above  equation.  This  constant  is  the  correction  for  position 
and  is  generally  designated  by  the  letter  C ;  we  therefore 
have  finally 

^0— (30  (^) 

Proceeding  now  to  discuss  the  structure  of  the  above 
function  of  /,  equation  (i),  it  should  be  remembered  that 
each  change  in  temperature  causes  two  different  forces  to 
act  on  the  mechanism.  In  the  first  place,  the  corrugated 
surface  of  the  vacuum  chamber  having  a  greater  area  than 
corresponds  to  its  circumference,  is  expanded  too  much  by 
a  rise  in  temperature,  and  this  excess  of  expansion  causes  a 
depression  of  the  surface.  The  reason  why  the  latter  is  not 
raised  instead  of  being  depressed  is  to  be  found  in  the  circum¬ 
stance,  that  in  all  good  instruments  it  is  bent  slightly 
towards  the  interior,  so  that,  even  under  a  minimum  of 
atmospherical  pressure,  it  will  only  rise  about  to  the  horizon¬ 
tal,  but  never  bulge  outward  beyond  this. 

The  second  force  is  created  by  the  small  quantity  of  air, 
present  in  all  so-called  vacuum  chambers,  being  expanded  by 
the  additional  heat  imparted  to  it,  thus  exercising  an  inside 
pressure,  that  tends  to  counteract  the  first  described  force. 

In  the  Naudet  aneroid  the  chamber  is  exhausted  as  much 
as  possible,  and  the  inside  pressure  caused  by  a  rise  of  tem¬ 
perature  under  all  ordinary  circumstances  is  therefore  miich 
smaller  than  the  force  caused  by  surface  expansion  of  the 
box  and  pressing  such  surface  towards  the  interior.  These 
instruments  will  therefore  be  affected  by  a  rise  of  tempera¬ 
ture  in  the  same  way  as  by  an  increase  of  atmospherical 
pressure,  that  is,  the  reading  of  the  instrument  will  become 
higher.  Hence  the  correction  for  temperature  in  Naudet 
aneroids  is  subtractive  for  all  temperatures  above  the  freez¬ 
ing  point  and  additive  for  all  temperatures  below. 

\ 

From  what  has  been  said,  it  is  clear  that  the  second  or 
inside  force  ean  be  increased  by  admitting  additional  air 


lO 


into  the  vacuum  chamber,  and  it  was  suggested  by  Professor 
Kohlrausch,  that  in  this  way  the  two  forces  might  be  made 
to  counterbalance  each  other  entirely,  thus  reducing  the 
correction  for  temperature  to  nothing.  The  impossibility  of 
this  was  demonstrated  bv  Professor  Weilenmann,  whose 
extensive  theoretical  and  experimental  researches  on  this 
subject  rendered  the  following  results  : 

( 1)  When  the  temperatures  are  plotted  as  ordinates  and 
the  corrections  pertaining  to  them  as  abscisses,  then  a  para¬ 
bola  is  obtained. 

(2)  The  apex  of  this  parabola  can  be  shifted  to  lower  or 
higher  temperatures,  by  respectively  increasing  or  diminish¬ 
ing  the  amount  of  air  contained  in  the  chamber. 

Although  these  principles  differ  theoretically  from  Bauern- 
feind’s  opinion,  that  the  correction  for  temperature  increases 
in  direct  proportion  to  the  temperature,  yet  for  Naudet 
aneroids,  with  highly  exhausted  chambers,  there  is  no  great 
practical  difference  between  both  assertions.  This  will  be 
seen  clearly  from  the  following  diagram,  in  the  left-hand 
part  of  which  a  correction  curve  for  temperature  is  shown, 
that  was  obtained  bv  Professor  Weilenmann  from  actual 
tests  with  an  aneroid,  the  chamber  of  which  was  exhausted 
as  completely  as  possible.  For  all  such  temperatures  as  are 
likely  to  occur  in  practical  work,  this  curve  does  not  depart 
materiallv  from  a  straight  line,  which  latter  would  be  the 
expression  of  Bauernfeind’s  law  in  the  diagram. 

TEMPERATURE  IN  IdEGREES  CELSIUS. 

Professor  Weilenm aim’s  above  named  principles  have 
been  utilized  in  the  construction  of  the  Goldschmid  aneroid 
for  the  purpose  of  reducing  as  much  as  possible  the  correc¬ 
tion  for  temperature.  An  amount  of  air  corresponding  to  a 
few  inches  of  the  mercurial  column  is  admitted  into  the 
vaccuum  chamber,  thereby  shifting  the  apex  of  the  parabola 
to  near  the  freezing  point  and  consequently  reducing  to 
practically  nothing  the  corrections  in  that  vicinity.  An 
example  of  this  is  given  in  the  right-hand  part  of  Fi^.  j, 
where  a  correction  curve  is  shown  for  a  vacuum  box,  which 
contained  an  amount  of  air  corresponding  to  six  inches 


of  the  mercurial  column.  The  characteristic  differences 
between  this  curve  and  the  high  vacuum  curve  in  the  left- 
hand  part  of  the  same  diagram,  are  at  once  apparent  and 
strikingly  to  the  advantage  of  the  former.  Under  the 
influence  of  high  temperatures  the  inner  pressure  now 
exceeds  the  force,  bending  the  surface  towards  the  in¬ 
terior,  in  other  words,  such  influence  will  act  on  the  Gold- 
schmid  aneroid  like  a  decrease  of  atmospheric  pressure. 

Summing  up,  we  find  that  the  correction  for  temperature 
for  the  Goldschmid  instruments  in  the  vicinity  of  the  freez¬ 
ing  point  is  practically  nothing,  again,  that  as  a  general  rule 
it  is  everywhere  considerably  less  than  for  the  Naudet 
aneroid  or  for  the  mercurial  barometer,  and,  finally,  that  what 
little  there  is  of  it,  is  additive. 

While  the  Goldschmid  aneroid  is  not  claimed  to  be 
entirely  compensated  for  temperature,  the  corrections  for 
the  latter  are  doubtless  in  it  reduced  to  very  small  quanti¬ 
ties,  a  table  of  which,  resulting  from  careful  tests  made  by 
the  manufacturer,  accompanies  every  instrument. 

For  some  of  the  Naudets  in  the  market,  entire  compen¬ 
sation  is  claimed,  but  if  the  practical  test  is  made,  probably 
one  out  of  ten  will  be  actually  found  so,  while  the  correc¬ 
tions  of  most  of  the  rest  will  exceed  those  of  the  Gold¬ 
schmid,  without  the  purchaser  being  furnished  with  a  table 
for  them. 

A  simple  and  very  effective  method  of  ascertaining  the 
correction  for  temperature  consists  in  the  use  of  warm,  tepid 
and  cold  water  baths,  and  finally  the  ice  bath.  By  their 
means  the  inner  temperature  of  an  instrument  can  be  varied 
from  the  freezing  point  upward,  to  say  ioo°  or  more.  The 
observations  must  of  course  be  made  together  with  obser¬ 
vations  on  a  mercurial,  and  both  are  recorded  in  about  the 
following  way : 


12 


Mercurial 

Thermometer. 

Aneroid. 

-^0 

A 

/ 

A' 

29094  —  A' 

I 

2 

3 

4 

5 

29149 

29-073 

670 

29-016 

0-078 

29'i48 

29*070 

66-2 

29*014 

0-080 

29-143 

29-073 

750 

29-022 

0*072 

29-132 

29-074 

74’4 

29*035 

0*059 

etc. 

etc. 

etc. 

etc. 

etc. 

In  this  table  the  letters  at  the  heads  of  the  various 
columns  have  the  following  meaning  : 

(1)  reading  of  the  mercurial  barometer  in  inches 
and  decimals,  as  reduced  to  the  freezing  point. 

(2)  A  is  the  reading  of  the  aneroid  under  the  same  pres¬ 
sure. 

(3)  t  is  the  inner  temperature  of  the  aneroid  in  degrees 
Fahrenheit  and  decimals. 

(4)  A'  is  what  the  aneroid  would  have  read,  if  the  pres¬ 
sure  during  the  entire  series  of  observations  had  constantly 
remained  at  B\  ==  29^094  (this  being  the  average  of  all  the 

of  the  entire  series). 

The  value  of  A' is  found  in  the  following  manner:  In 
the  case  of  the  actual  example  cited  here  a  preliminary 
determination  had  been  made,  showing  that  rooo  inch  of 
the  aneroid  corresponded  to  0*970  inch  of  the  mercurial 
column.  If,  therefore,  in  the  case  of  the  first  observation 
for  instance,  the  mercurial  barometer  had  read  29*094  (instead 
of  29*149),  that  is  0*055  l®ss  than  it  actually  did  read,  then 
the  aneroid  would  clearly  have  read  X  0*055  =  0*057  less 
than  it  actually  did  read,  that  is  to  say  29*073 — 0*057  = 
29*016.  The  difference  between  the  value  29*094 — A'  as 
found  for  the  freezing  point  and  as  found  for  any  other 
temperature  renders  the  correction  for  such  temperature. 
These  differences  should  be  found  for  the  various  tempera¬ 
tures  from  the  freezing  point  upward  to  say  100°  F.,  and 
then  plotted,  as  shown  in  Fig.j;  from  the  curve  thus  obtained 
a  table  of  corrections  is  easily  deduced. 


13 


The  correction  for  graduation  has  been  assumed  in  equa¬ 
tion  (2)  to  stand  in  direct  proportion  to  the  difference  30. — 
Reading,  an  assumption,  which  although  not  strictly  correct 
is  sufficiently  so  for  most  practical  purposes. 

Each  Goldschmid  aneroid  being  furnished  with  a  table 
of  corrections  for  graduations,  as  well  as  for  temperature, 
the  owner  of  one  of  these  instruments  is  saved  the  trouble 
of  investigations  in  this  respect. 

For  Naudet  aneroids  these  tables  have  to  be  obtained  by 
the  purchaser,  through  direct  comparison  of  the  aneroid 
with  the  mercurial  barometer,  the  readings  of  both  being 
reduced  to  the  freezing  point  by  means  of  the  previously 


hjghly  Exhaust.  /50^^'of  A/r 


determined  correction  for  temperature.  The  observations 
are  recorded  in  tabulated  form  as  follows : 


^0 

A 

\ 

t 

•^0 

0 

1 

0^ 

29‘97o 

29 '960 

72 

30*000 

0-030 

29‘420 

29 ‘450 

76 

29-500 

0-080 

28'87o 

28 '940 

78 

29*000 

0-130 

wherein  the  various  letters  have  the  same  meaning  as  in 
equations  (i)  and  (2).  From  the  table  it  is  seen  that  in  this 
case  the  constant  correction  for  position  was 

0-03 

and  that  1*000  inch  of  the  aneroid  correspond  to  rioo  inch 


14 


of  the  mercurial ;  the  coefficient  of  graduation  therefore 
was 

y9  =  — 0-100 

and  by  means  of  these  figures  a  table  of  corrections  for 
graduation  can  easily  be  worked  out  according  to  equa¬ 
tion  (2). 

But  if  it  is  desired  to  use  the  aneroid  at  great  altitudes, 
then  it  would  not  be  safe  to  assume  the  coefficient  /9  to 
remain  constantly  the  same,  and  the  investigation  should 
in  this  case  be  extended  to  lower  pressures,  either,  by  * 
making  comparisons  between  the  mercurial  barometer  and 
the  aneroid  at  various  altitudes,  or  by  making  them  by 
means  of  the  air-pump.  If  the 'latter  method,  however,  is 
selected,  then  a  certain  correction  of  the  results  will  have 
to  be  made,  the  nature  of  which  is  explained  by  Dr.  C. 
Koppe  as  follows: 

Suppose  an  aneroid  and  a  mercurial  barometer  to  be  at  the 
same  locality  and  subjected  to  the  same  atmospheric  pres¬ 
sure,  and  again  suppose  a  sudden  decrease  of  the  force  of 
gravity  to  take  place  there.  What  influence  would  such  an 
event  have  on  the  reading  of  the  two  instruments  ? 

Manifestly  the  reading  of  the  mercurial  barometer  would 
not  be  affected  in  the  least,  the  weight  of  the  column  of  air 
being  diminished  in  the  same  ratio  as  that  of  the  mercurial 
column. 

It  would  be  quite  different,  however,  with  the  aneroid. 
While  the  weight  of  the  column  of  air  has  diminished,  the 
elastic  force  of  the  vacuum  chamber  has  remained  the  same ; 
the  instrument  will  therefore  record  a  lower  pressure. 

Consequently,  if  a  journey  is  undertaken  with  an  aneroid 
and  a  mercurial  barometer,  which  read  precisely  alike,  then 
the  coincidence  between  both  will  only  last  as  long  as  the 
force  of  gravity  remains  unchanged.  But  this  force  is 
different  in  different  latitudes,  and  at  different  altitudes,  and 
from  the  latter  circumstance  results  the  necessity  of  a  cor¬ 
rection  of  such  tables  for  graduation,  that  were  obtained 
by  means  of  the  air-pump. 

It  is  clear  from  the  above  that  a  reading  of  twenty-four 
inches  of  the  mercurial  barometer,  taken  at  the  level  of  the 


15 


sea  under  an  air-pump,  indicates  a  greater  actual  pressure  of 
air  than  the  same  reading  taken  at  an  altitude  of  7,000  feet 
above  the  level  of  the  sea.  Hence,  a  correction  has  to  be 
added  to  the  reading  of  the  aneroid  at  7,000  feet  altitude,  in 
order  to  obtain  coincidence  of  such  reading  with  the  mercu¬ 
rial  barometer.  The  amount  of  this  correction  has  been 
computed  by  Professor  Weilenmann  as  follows : 

Reading  (inches), .  31*5  28*0  24*0  20‘o  i6'o 

Correction,  .  .  .  o  +0-105  +0*189  +0-270  +0-312 

The  arithmetical  sums  of  these  figures  and  the  corre¬ 
sponding  corrections  found  by  means  of  the  air-pump  are 
the  final  corrections  for  graduation. 

The  difficulty  caused  by  “  elastic  reaction,”  which  was 
mentioned  in  the  beginning  of  this  article  is,  of  course, 
present  also  in  the  Goldschmid  aneroid,  and  the  above 
investigations,  as  well  as  all  measurements  of  altitudes, 
should  be  carried  on  with  due  regard  to  it.  The  instru¬ 
ment  must  be  given  time  in  order  to  fully  accommodate 
itself  to  any  sudden  changes  of  pressure. 

But  while  Kroeber  found  that  the  Naudet  required  days 
for  this,  he  found  the  Goldschmid  practically  accommodated 
after  one  or  two  hours.  Again,  he  found  the  extreme  dif¬ 
ferences  resulting  from  elastic  reaction  in  the  latter  instru¬ 
ment  only  about  one-fourth  of  those  in  the  former.  Both 
these  advantages  of  the  Goldschmid,  as  compared  with  the 
Naudet,  are  doubtless  due  to  the  extreme  simplicity  of  the 
former’s  mechanism,  and  in  view  of  them  it  may  be  safely 
asserted  that  the  gradual  changes  of  pressure,  taking  place 
during  ordinary  explorations  of  mountainous  country,  will 
not  produce  any  appreciable  errors  of  elastic  reaction  in  the 
Goldschmid  aneroid. 

V.  THE  DETERMINATION  OF  DIFFERENCES  OF  ALTITUDE  BY 
MEANS  OF  THE  ANEROID  BAROMETER. 

The  measuring  of  altitudes  by  means  of  the  barometer, 
is  mainly  based  on  two  suppositions,  viz  :  Firstly,  that  the 
atmospheric  strata  of  equal  pressure  are  horizontal,  and 
secondly,  that  the  temperature  of  a  vertical  column  of  air  is 


i6 


N 


% 

equal  to  the  arithmetical  mean  of  the  temperature  observed 
at  its  top  and  at  its  bottom. 

These  two  conditions  are  probably  never  fulfilled  com¬ 
pletely  in  nature,  but  they  are  always  fulfilled  more  or  less 
approximately.  On  the  g-reater  or  smaller  deviation  from 
them  of  the  actually  existing  conditions,  depends  the  exacti¬ 
tude  of  the  result  in  each  case,  leaving  out  the  considera¬ 
tion,  of  course,  of  avoidable  errors  of  observations. 

In  accordance  with  the  two  principles  mentioned,  the 
process  of  barometric  measurement  may  be  described  thus : 
By  means  of  the  barometer,  be  it  a  mercurial  or  be  it  an 
aneroid,  the  weight  of  a  column  of  air  is  determined,  and 
from  the  observed  temperature  of  such  column  its  length  is 
found. 

During  observations  for  altitude,  therefore,  the  tempera¬ 
ture  of  the  air  as  well  as  that  of  the  instrument  must  be 
observed ;  the  first  one  for  the  purpose  named  just  now,  the 
last  one  for  the  purpose  of  taking  into  proper  account  the 
x:orrections  for  temperature,  by  reducing  both  observations 
to  uniform  temperature.  Besides  this,  the  observations 
made  at  the  upper  and  at  the  lower  stations  must  of  course 
be  corrected  to  graduation,  so  that  thus  their  difference  is 
made  equal  as  nearly  as  possible  to  the  difference  that  would 
have  been  obtained  by  using  a  mercurial  barometer. 

It  is  clear  at  once  that  the  observations  at  the  upper  and 
lower  stations  should  be  made  simultaneously  in  order  to 
obtain  both  as  nearly  as  possible  under  the  same  atmos¬ 
pheric  conditions.  Observations  made  by  one  observer,  in 
passing  from  point  to  point  with  his  instrument,  are  quite 
unreliable,  unless  he  returns  to  the  previous  point  after  each 
observation  in  order  to  take  a  second  reading  there,  and 
thus  to  find  the  changes  that  have  taken  place  in  pressure 
and  temperature.  Only  by  means  of  this  tedious  and  time¬ 
robbing  procedure,  can  anything  like  fair  results  be  obtained 
by  one  observer. 

For  serious  work  then,  two  observers,  and  at  least  two 
instruments  are  required,  and  the  readings  of  the  latter,  as 
well  as  the  outer  and  inner  temperature,  should  be  recorded 
with  great  exactitude,  so  as  to  be  enabled  to  subsequently 


17 


introduce  the  proper  corrections,  without  which  the  results 
are  worthless.  Great  care  also  should  be  taken  not  to  expose 
•the  aneroid  to  the  direct  rays  of  the  sun  when  taking  an 
observation,  but  to  let  it  assume  as  nearly  as  possible  the 
temperature  of  the  .surrounding  air  in  the  shadow. 

The  modus  operandi  in  determining  differences  of  altitude 
may  be  described  about  as  follows ; 

A  stationary  instrument,  with  an  observer,  is  placed  at  some 
point  of  known  altitude  that  has  been  selected  as  the  basis 
of  operations.  This  instrument  is  observed  regularly  every  , 
fifteen  or  thirty  minutes,  and  a  careful  record  kept  of  such 
readings,  as  well  as  of  the  time  and  temperature  correspond¬ 
ing  to  each. 

Meanwhile,  the  engineer  travels  through  the  district  he 
intends  to  survey,  taking  observations  wherever  he  sees  fit, 
and  keeping  a  careful  record  of  their  location,  time,  temper¬ 
ature,  etc.  When  he  is  through  with  his  work,  an  observa¬ 
tion  at  the  point  of  known  altitude  is  computed  for  each  of 
his  observations,  from  the  record  kept  by  the  assistant ;  this 
having  been  done,  the  difference  of  altitude  between  each 
point  of  observation  and  the  point  of  known  altitude  is 
obtained  in  a  simple  way,  by  means  of  the  subjoined  table 
No.  I,  which  has  been  taken  from  Meteorological  and  Physical 
Tables  of  the  Smithsonian  Institution.  [Other  convenient  tables 
are  given  in  The  Aneroid  Barometer,  Van  Nostrand,  New 
York,  1888,  and  in  the  above  mentioned  publication  of  the 
Smithsonian  Institution.] 

For  instance,  suppose  29*5  to  have  been  the  reading  at 
the  point  of  known  altitude,  and  26*5  the  reading  taken  by 
the  engineer,  both  corrected  to  graduation,  etc.,  and  reduced 
to  32"^  F.,  and  again,  suppose  70°  and  60°  to  have  been  the 
respective  temperatures  of  the  surrounding  air,  then  we 
obtain  from  the  table ; 


For  29*5  inches  and  70°  F .  96'5 

For  26'5  inches  and  60°  F,, . 

Mean,  . ioo’9 


This  mean,  multiplied  by  the  difference  of  the  two  read- 

2* 


i8 


ing-s  expressed  in  tenths  of  an  inch,  renders  the  difference 
in  altitude : 

30  X  100*9  3,027  ft. 

The  use  of  this  table  gives  results  of  sufficient  accuracy 
for  all  practical  purposes,  so  that  recourse  to  the  compli¬ 
cated  barometrical  formula  is  not  required. 

Readings  should  always  be  taken  in  the  same  position  of 
instrument,  preferably  the  horizontal  one. 

Table  No.  i. 

HEIGHT  IN  FEET  OF  A  COLUMN  OF  AIR  CORRESPONDING  TO  ONfe-TENTH  OF  AN  INCH  IN  THE 

BAROMETER. 


Barometer 
Reading  in 
Inches. 

Temperature  of  Air  in  Degrees  Fahrenheit. 

0 

0 

50“ 

60° 

70° 

00 

c 

P 

1 

90° 

23-0 

Ii6'2 

ii8-8 

121-3 

1238 

1  . 126-4 

129-9 

23  5 

i^3’7 

1i6'2 

118-7 

121*2 

123-7 

126  I 

24*0 

111-3 

113-8 

I  i6-2 

1 18'6 

121  *1 

123-5 

24-5 

log  - 1 

Ill's 

113  8 

h6-2 

118-6 

121-0 

25-0 

io6'9 

109-3 

1 1 1'6 

113-9 

116-3 

118  6 

25*5 

1 04 ‘8 

107*1 

109-3 

111-6 

113  9 

1 16-2 

260 

102’7 

1050 

107-2 

109-5 

111*7 

114*0 

26-5 

ioo'g 

103-1 

105-3 

107-5 

109-7 

11 1-8 

27*0 

gyo 

101*2 

103-3 

105-5 

107-6 

109-8 

27*5 

97  2 

993 

101*4 

103-5 

105-6 

107  8 

28’0 

95'4 

97'5 

99  6 

ioi'7 

103-8 

105-9 

28-5 

93-8 

95-8 

97-9 

99-9 

loi  '9 

103-9 

29*0 

92*1 

94’ I 

96-2 

98-2 

IOO'2 

102*2 

295 

906 

r  92-5 

94-5 

96-5 

98-5 

100*4 

30  0 

89-1 

91*0 

92-9 

94-9 

96-8 

q8-8 

30  5 

876 

89-5 

91-4 

93-3 

95-2 

97  2 

Table  No.  2. 

REDUCTION  OF  MERCURIAL  COLUMN  TO  32°  F.,  BRASS  SCALE  TO  BAROMETERS  CORRECT  AT  62°  F. 


Reading  of  Barometer. 

Tempera- 

ture. 

30  inches. 

25  inches. 

20  inches. 

32° 

-009 

•co8 

-006 

35° 

■017 

-015 

‘012 

40° 

-031 

-026 

*021 

45° 

-044 

.  -037 

*030 

50° 

-058 

-048 

-038 

55° 

*071 

-059 

-047 

60O 

-084 

070 

-056 

(^5° 

-098 

-082 

-065 

^  70° 

*  1  II 

-093 

-074 

v  ^.0 

-125 

*104 

-083 

80O 

■138 

-115 

’092 

85O 

■151 

-126 

'lOI 

90^’ 

-164 

-137 

-no 

95° 

-178 

-148 

-118 

100° 

-191 

• 

-159 

-127 

The  corrections  contained  in  this  table  have  to  be  sub¬ 
tracted  from  the  reading-  of  the  mercurial  barometer,  in  order 
to  reduce  the  same  to  a  temperature  of  32^  F. 


Wl.  I?. 


